Having clung on through the worst housing slump in decades, Britain's housebuilders are back in the black and their shares are again sought-after in the City. Taylor Wimpey, which nearly collapsed under its debts three years ago, swung to an annual profit last week and cheered investors by announcing its first dividend since 2007 – albeit just 0.38p a share.

Persimmon, which owns the Westbury and Charles Church brands, went further and pledged to return £1.9bn, or £6.20 a share, to shareholders in the coming nine and a half years, sending its stock soaring.

The housing boom saw housebuilders ramp up construction just as the financial crisis struck in 2008. Much chastened, they now seem happy building far fewer homes, with a shift away from apartments towards larger family houses. David Ritchie, chief executive of Bovis Homes, echoed the general feeling in the sector when he talked of static sales levels, flat prices and stagnant mortgage approvals being the "new norm" last week. "The housing market is remarkably stable but at low levels of activity," he said.

The extent of the general downturn in construction is illustrated by official figures showing new orders slumped to their lowest level since 1980 last year. The only sector in which orders rose was private housing, up 6%.

The heady boom days of 2007 are clearly over, but all the listed housebuilders are profitable again. Analysts at Investec give the thumbs-up to the sector, which they say is "huffing and puffing" on the road to recovery. The firm's Mike Bessell says: "What has really changed from 2008/2009 and even early 2010 is that housebuilders are in control of their destiny."

Housebuilders have good reasons to be fairly optimistic. The UK housing shortage is apparently getting worse rather than better. By 2015 demand for housing will outstrip supply by more than 500,000 homes, according to the Federation of Master Builders (FMB), partly due to delays in the planning system. First-time buyers are still struggling to get on the housing ladder and the impact of this has been fewer homes being built, despite the pent-up demand, it argues.

Just 115,000 permissions to build homes were granted in 2011, half the 2006 level and half the number required, according to building data firm Glenigan.

Changes to the planning system will be crucial to how quickly homes can be built in future. The industry is anxiously awaiting the government's new national planning policy framework, due in weeks. The Home Builders Federation is calling on the government to resist the "vocal anti-development lobby's scaremongering".

Sir Bob Kerslake, head of the civil service and permanent secretary to the communities department, last week confirmed that the framework would include a presumption in favour of sustainable development.

Meanwhile, the FMB is urging the chancellor to use his budget to extend the stamp-duty holiday for first-time buyers on properties under £250,000, due to expire later this month. Even so, this year could be good for first-timers, if the government-underwritten NewBuy scheme is successful. From this month, it will allow people to get a mortgage with only a £10,000 deposit for a newly built property priced up to £500,000. The prime minister has suggested this could help 100,000 would-be buyers who are struggling to raise the average deposit demanded by lenders of £40,000, though critics argue that it is better news for builders than borrowers.

Housebuilders are certainly rubbing their hands. Pete Redfern, chief executive of Taylor Wimpey, believes it could have a "material impact". "Most of the major lenders will be involved," he says. "The biggest constraint in the short term is mortgage availability."

Mortgage approvals hit a 25-month high in January, but the worry is that first-time buyers are just trying to beat the end of the stamp duty holiday. Shared-equity schemes such as FirstBuy – where the government and the developer invest equal amounts and the buyer only has to contribute a cash deposit of 5% – have also underpinned demand.

Housebuilders have also improved returns by snapping up land without planning permission cheaply and paying for it only after getting the green light for development. In some cases, they even buy farmland at agricultural prices and let it back out.

So is everything tickety-boo again? Brokerage Collins Stewart thinks not. Housing analyst Alastair Stewart, one of the City's most bearish voices, has warned that UK housing could be stuck in a "lost decade", with mortgage lending, transactions and prices all likely to fall this year. "Housing could remain caught between weak consumer appetite for borrowing and banks' aversion to mortgage lending largely due to eurozone risks."

He claims Britain's housing shortage is not as bad as it is purported to be, arguing that the housing stock has gone up by almost twice the rate of population growth since 1991.

Steve Morgan, the outspoken chairman and founder of Redrow who also owns Premier League football club Wolverhampton Wanderers, dismisses this as a "load of bollocks" and others in the City cast doubt on Stewart's calculations, saying they do not appear to account for immigration, the trend towards one- and two-bedroom households, and removal of old houses.

And Investec's Bessell does not expect any material shocks to house prices over the next couple of years. He says the housing market has already reached "something of a nadir, with a very low level of activity which represents little, if anything, more than the transactions of the 'must movers' in the market".